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Refinement monoids with weak comparability and applications to regular rings and $C^*$-algebras

Author(s): P. Ara; E. Pardo
Journal: Proc. Amer. Math. Soc. 124 (1996), 715-720.
MSC (1991): Primary 16E20, 16E50, 46L80, 19K14, 06F20
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Abstract: We prove a cancellation theorem for simple refinement monoids satisfying the weak comparability condition, first introduced by K.C. O'Meara in the context of von Neumann regular rings. This result is then applied to von Neumann regular rings and $C^*$-algebras of real rank zero via the monoid of isomorphism classes of finitely generated projective modules.

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Additional Information:

P. Ara
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
Email: para@mat.uab.es

E. Pardo
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain -
Email: epardo@mat.uab.es

DOI: 10.1090/S0002-9939-96-03059-6
PII: S 0002-9939(96)03059-6
Keywords: Refinement monoid, $C^*$-algebra with real rank zero, von Neumann regular ring, weak comparability
Received by editor(s): May 19, 1994
Received by editor(s) in revised form: September 21, 1994
Additional Notes: The research of the authors was supported by grants from the DGICYT (Spain).
Dedicated: Dedicat al petit Guillem
Communicated by: Ken Goodearl
Copyright of article: Copyright 1996, American Mathematical Society

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